A148391 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 0, 1), (0, 0, -1), (0, 1, 0), (1, -1, 1)}.

1, 1, 2, 5, 16, 52, 170, 581, 2082, 7647, 28508, 107906, 414484, 1611854, 6332018, 25103351, 100354887, 404032355, 1636789195, 6669626502, 27324758600, 112493883858, 465159225696, 1931115979433, 8047040424824, 33649572444003, 141165249544075, 593988710389378, 2506331355166934

Offset

0,3

Links

Table of n, a(n) for n=0..28.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A011819 A148390 A232317 * A337268 A148392 A149956

Adjacent sequences: A148388 A148389 A148390 * A148392 A148393 A148394

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved